What are the belt rankings in Brazilian Jiu JItsu?

As with other martial arts, a student's progress is marked with a series of colored belts. In Brazilian Jiu Jitsu, the rank of Black Belt is conferred to individuals who have mastered the art of Brazilian Jiu-Jitsu.
The belts in order are: White, Blue, Purple, Brown and Black. Some schools also award four stripes to mark a student's progress from White through Brown belts. Black Belts are typically awarded one stripe every three years up to ten stripes. There are special classifications for Black Belts fighter and instructors. Instructors have Black Belts with Red bands and Black Belt fighters have White Bands. Typically, Black Belt instructors are not allowed to promote others up to Black Belt rank until they receive their first stripe.
The ranks for children are different. Blue belt and higher ranks have age requirements so children have the following ranks beginning with Gray, Yellow, Orange and Green. Each belt has 4 stripes. These belts are utilized until age 16.
You can find a chart of the International Brazilian Jiu Jitsu Federation's belt ranking system at: http://ibjjf.org/wp-content/uploads/2014/02/IBJJF-Graduation-System-Poster.pdf

What are the rules for sparring at Samurai BJJ?

What are the rules for sparring at Samurai BJJ?

For the purposes of sparring at our gym, we follow the IBJJF rule set by default. In other words, training partners may always use the techniques permissible at the lower-ranked training partner's belt level. Thus, if a brown belt is training a blue belt, both would use the techniques that are legal under IBJJF rules at the blue belt level. However, we do permit training partners at blue belt and above to agree to use other techniques, such as footlocks and heelhooks if they both agree to do so.
Regardless of belt rankings, rule sets, or agreements between students, we require all students always to train with their partner's and their own safety in mind, as well as the safety of others who may be training on the mat at the same time. Accordingly, if you are applying a submission, it is your responsibility to provide your training partner with a fair opportunity to tap out before they are injured and to release the submission immediately in a safe manner after the training partner taps. Likewise, if you are defending a submission, it is your responsibility to protect yourself by verbally and physically tapping out before you are injured. It is always better to err on the side of caution. It is far better to release a submission early before your training partner taps rather than risking injury to your partner. By the same token, it is always better to tap early rather than risk injury to yourself.
The following "techniques" are NEVER permitted:

Finger/Thumb/Toe/small joint manipulations, crushes, breaks, twists or anything else intended to injure the digits of the hand or foot.

Biting

Spiking, slamming or picking up and dropping your training partner

Intentionally throwing or pushing your training partner into a wall or off of the mat

Punching, striking or kicking any part of your training partner's body

You get the idea. Don't do dirty stuff to your training partner that you wouldn't want them doing to you.

What are the rules of Brazilian Jiu Jitsu and submission grappling?

What are the rules of Brazilian Jiu Jitsu and submission grappling?

Depending on the sponsoring organization, the rules for BJJ and Submission Grappling competitions can vary significantly.
For example, the IBJJF and other organizations ban the use of heel hooks, neck cranks and slamming your opponent to the mat when competing in the gi, regardless of rank. Other techniques, such as ankle locks, toe-holds, and knee bars become legal at various points at purple belt and above.
For Submission Grappling events, however, heel hooks and neck cranks are often perfectly legal, especially at the higher levels of competition.
For the purposes of sparring at our gym, we follow the IBJJF rule set by default. In other words, training partners may always use the techniques permissible at the lower-ranked training partner's belt level. Thus, a brown belt training with a blue belt would both use the techniques that are legal at the blue belt level. However, we do permit training partners at blue belt and above to agree to use other techniques if they both agree to do so.
Regardless of belt rankings, rule sets, or agreements between students, we require all students always to train with their partner's and their own safety in mind, as well as the safety of others who may be training on the mat at the same time. Accordingly, if you are applying a submission, it is your responsibility to provide your training partner with a fair opportunity to tap out before they are injured and to release the submission immediately in a safe manner after the training partner taps. Likewise, if you are defending a submission, it is your responsibility to protect yourself by verbally and physically tapping out before you are injured. It is always better to err on the side of caution. It is far better to release a submission early before your training partner taps rather than risking injury to your partner. By the same token, it is always better to tap early rather than risk injury to yourself.

What is Brazilian Jiu Jitsu?

The history of modern Brazilian Jiu-Jitsu begins with Mitsuyo Maeda, a prominent Japanese Judoka and member of the Kodokan.
Maeda was one of several judoka (Maeda, Satake, Okura, Shimitsu, and Laku) sent by Jigoro Kano, the founder of Judo, to demonstrate Judo around the world, including the United States, Europe and South America. Although Maeda is usually the focus of Brazilian Jiu Jitsu's early history (because he taught Carlos Gracie), it must be noted that Soshihiro Satake was the first Japanese to open a Judo/Jiu Jitsu academy in Brazil.
In any event, Maeda is said to have fought over 2,000 matches in his career, many unrecorded. He traveled throughout the Americas and Europe. Because Maeda was only 5'4", his opponents were usually far larger than he was. Notably, Maeda was not undefeated. He lost two matches in the catch-as-catch-can world championships held in London, where Maeda entered both the middleweight and heaveyweight divisions, advancing to the semi-finals and finals respectively. In matches where judo gis were worn, however, Maeda was undefeated.
In 1914, Maeda traveled to Brazil for the first time and for the next seven years he would constantly be visiting the South American nation fighting challenge matches. In 1921 Maeda opened his own Judo academy in Brazil, which still exists today. Two of his most famous students were Carlos Gracie (Helio Gracie's older brother) and Luiz França Filho, who began his training in Manaus with Satake. Maeda taught the training methods of Kodokan Judo, with its emphasis of live randori (sparring) and newaza (groundfighting), as well as classical submission holds that were not part of the traditional Judo curriculum. In addition, photographs suggest that Maeda also taught catch wrestling techniques, which he undoubtedly learned and absorbed from his extensive fighting career abroad.
Carlos Gracie took his first lessons in what Maeda then called "Kano Jiu Jistu" at age 14. Although it is unclear how long Carlos actually trained with Maeda (probably less than 4 years), Carlos opened the first Gracie-owned Jiu Jitsu academy in Rio with his first students being his younger brothers: Oswaldo, Gastao, George and Helio Gracie.
The Gracie's primary innovation to what they learned from Maeda seems to have been their focus on the Newaza (groundfighting) aspect of Judo and development of the dō-osae or trunk position, which became what is today known as the guard.

What makes Brazilian Jiu Jitsu different from other martial arts?

Brazilian Jiu-Jitsu differs from other traditional martial arts (e.g., Karate, Tae Kwon Do, Kung Fu and Kenpo) in several ways. First, Brazilian Jiu Jitsu evolved to provide solutions for physically smaller and weaker individuals who face larger and stronger opponents. In contrast, success in traditional martial arts is often predicated on the student's strength, speed, size and power. Second, Brazilian Jiu Jitsu offers solutions to all phases of unarmed combat and self-defense, whether standing or on the ground. Most traditional martial arts focus almost entirely on stand-up techniques and ignore grappling altogether. Third, Brazilian Jiu Jitsu has a training method of live-grappling sparring (similar to Judo and Wrestling) that is based on the performance of technique on a resisting training partner, who is doing his or her best to avoid defeat and attain victory. Many traditional martial arts are learned almost exclusively through kata, a prearranged set of movements executed on a cooperative training partner and/or no-contact sparring.

What's a Typical Class Like?

Classes begin with light calisthenics and stretching, followed by technique-based drilling. After the warm-up, the instructor will teach 2-3 specific and usually inter-related techniques. Students will perform drills and other exercises designed to help them retain the technique. After drills, students will spar (or roll), putting their techniques to the test with training partners who can resist and counter just as they would in an actual fight, providing valuable real-world experience should the techniques ever need to be applied in an actual fight.